Vice President-elect Mike Pence on Wednesday called for a swift but “smooth” repeal of the Affordable Care as President Barack Obama visited Capitol Hill in the hopes of protecting his signature legislative achievement against a GOP agenda set on dismantling it.

"The first order of business is to repeal and replace Obamacare, and that was our message today and that will be our message on Capitol Hill," Pence told reporters after meeting with Congressional Republicans.

Ahead of Pence's press conference with Congressional leadership, the president-elect went on a Twitter rant blaming Democrats for "massive increases" in premiums and saying the law will "fall of its own weight."

Republicans must be careful in that the Dems own the failed ObamaCare disaster, with its poor coverage and massive premium increases......

Simultaneously, Obama visited lawmakers on Capitol Hill to urge them to defend the law that has provided 20 million Americans with insurance.

“He said, 'Listen, don't mistake my cool demeanor for a lack of outrage. I'm angry just like you are about what has happened in the election and after the election.' And I think you could sense that he, you know, is maybe feeling a little forlorn that he's not going to be in this fight in the way that we are,” Democratic Sen. Chris Murphy said on MSNBC after the private meeting.

Another source in the room said the president lamented that he will soon be a private citizen because “I would love to be on the field.”

Republicans began what is expected to be an arduous process of following through on repealing and replacing Obamacare the same day a new Congress was sworn in. Though the GOP will soon control the White House, Senate and House of Representatives, they have yet to rally behind a single replacement plan.

Pence signaled the first steps the GOP will take is continuing to make the case against the Affordable Care Act, which Democrat Hillary Clinton also pledged to modify during the 2016 campaign.

And while calling Obamacare’s repeal a top priority for the incoming Trump administration, Pence also cautioned that lawmakers must ensure an "orderly and smooth transition" to a new healthcare system before full repeal.

"It will be important that we be careful that ... we do that in a way that doesn't work a hardship on American families that have gained insurance through this program. That it doesn't work a hardship on this economy," Pence said.

House Speaker Paul Ryan also said Republicans don't want to "pull the rug out from people."

Senate Minority Leader Chuck Schumer said Republicans are like “the dog that caught the bus" — able to repeal Obamacare but not sure how to replace it.

“Republicans say repeal and replace. The only thing that has going for it is alliteration,” House Minority Leader Nancy Pelosi said. “They have no replacement plan.”

Andrew Rafferty

Andrew Rafferty has been a political reporter for NBCNews.com since 2013. Rafferty writes and reports on politics for the web, and shoots and produces video for all NBC platforms.

Prior to joining NBCNews.com, Rafferty was a campaign reporter covering the 2012 presidential election. Rafferty was on the road for both the Republican primaries and general election, providing content for both the web and television.

Rafferty began at NBC News through a fellowship at "Meet The Press."

He is from Buffalo, N.Y., and attended John Carroll University in Ohio.